| 1850
...similar to those acts by which, knowing the previous propositions of Euclid, he might be assured that **the angle at the centre of a circle is double the angle at the circumference,** both angles standing on the same arc. On the contrary, our author would entirely exclude mathematical... | |
| Isaac Dalby - 1807
...must be equal. Coral. Hence equal chords in a circle, subtend equal anglei at the circumference. 71. **The angle at the centre of a circle is double the angle at the circumference when** both of them stand on the same arc. Let G4\C be an angle at the centre, and GPA an angle at the circumference.... | |
| Charles Hutton - 1811
...the arc AEB ; and thus, having equal measures, they are equal to each other (ax. 11). THEOREM LI. An **Angle at the Centre of a Circle is Double the Angle at the Circumference, when** both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,... | |
| Peter Fleming - 1815 - 164 sider
...equal to the opposite and inward angle, 4. The angles at the base of an isoceles triangle are equal, 5. **The angle at the centre of a circle, is double the angle at the circumference, when** standing upon the same arc of that circumference, ..---_ 6. The three angles of a triangle are equal... | |
| Charles Hutton - 1816
...the arc AFB ; and thus, having equal measures, they are equal to each other (ax. 11). THEOREM LI. AN **Angle at the Centre of a Circle is Double the Angle at the Circumference, when** both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,... | |
| 1816
...perpendicular to a tangent at the point of contact, that line paffes through the centre. THEOR. XXf.yfif.j?. An **angle at the centre of a circle is double the angle at the circumference** •which Hands upon the fame arch. Let ACB he the angleat the centre of a circle and ADB an angle at... | |
| Charles Hutton - 1822
...the arc AEB ; and thus, having equal measures, they are equal to each other («. 11). THEOREM Lt AN **Angle at the Centre of a Circle is double the Angle at the Circumference, when** both stand on the Same Arc. Let c be an angle at the centre c, and D an angle at the circumference,... | |
| Euclid, Dionysius Lardner - 1828 - 324 sider
...impossible. PROPOSITION XX. (355) The angle (ACD) at the centre of a circle, is double the angle (ABD) **at the circumference, when they have the same part of the circumference for their base. 1°. Let** the centre be on AB a side of the angle ABD at the circumference. Because in the triangle DCB the sides... | |
| Ferdinand Rudolph Hassler - 1828 - 159 sider
...-angle at the centre, and to these equal angles equal arcs will correspond. § 49. THEOREM. The an^le **at the centre of a circle is double the angle at the circumference,** that is subtended by the same chord or arc. APPLIC. In the circles ADBE, (fig. 53 and 54,) let the... | |
| Euclid - 1833 - 183 sider
...PROP. XX. THEOR. Fig. 27,23, The angle (ACD) at the centre of a circle is double °f th0 angle (ABD) **at the circumference, when they have the same part of the circumference for their base.** e N Fig. 27. (1) Prop. 5. B. 1. (2) Prop. 32. B. 1. Fig. 28. 1. Let one leg of the angle at the circumference... | |
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